Fig. 4.

Dynamics of the nested model when the therapeutic treatment failed. A, B The bacterial population (treated and untreated) with respect to time $\tau$ and resistance level x. C The basic reproduction numbers at the within-host level ${\mathcal{N}}_0^T(x)$ and ${\mathcal{N}}_0^U(x)$, with and without drug respectively. D The average resistance level ${\overline{x}}^{\vartheta }(\tau )$, $\vartheta \in \{T,U\}$ of the infected host. E The average resistance level $\eta (t)$ of the host population. F–H The between-host dynamics with respect to the treatment rate where ${\mathcal{R}}_0=10.9451$, 9.5855 and 8.2259, respectively. Parameter values are $({\sigma }_0,m_0,k_0,p_1/p_0,k_1/k_0,\mu )=(0.05,0.05,3,0.5,0.01,0.8598)$ and $\mathrm{\Lambda }=5\text{e}4$, ${\mu }_h=5.2675\text{e}-2$, ${\beta }_0=1.2\text{e}-3$, ${\alpha }_0=7.5\text{e}-2$, $\theta =1$, $r_0=9\text{e}3$